8z^2+20z-49=0

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Solution for 8z^2+20z-49=0 equation:


Simplifying
8z2 + 20z + -49 = 0

Reorder the terms:
-49 + 20z + 8z2 = 0

Solving
-49 + 20z + 8z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-6.125 + 2.5z + z2 = 0

Move the constant term to the right:

Add '6.125' to each side of the equation.
-6.125 + 2.5z + 6.125 + z2 = 0 + 6.125

Reorder the terms:
-6.125 + 6.125 + 2.5z + z2 = 0 + 6.125

Combine like terms: -6.125 + 6.125 = 0.000
0.000 + 2.5z + z2 = 0 + 6.125
2.5z + z2 = 0 + 6.125

Combine like terms: 0 + 6.125 = 6.125
2.5z + z2 = 6.125

The z term is 2.5z.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5z + 1.5625 + z2 = 6.125 + 1.5625

Reorder the terms:
1.5625 + 2.5z + z2 = 6.125 + 1.5625

Combine like terms: 6.125 + 1.5625 = 7.6875
1.5625 + 2.5z + z2 = 7.6875

Factor a perfect square on the left side:
(z + 1.25)(z + 1.25) = 7.6875

Calculate the square root of the right side: 2.772634127

Break this problem into two subproblems by setting 
(z + 1.25) equal to 2.772634127 and -2.772634127.

Subproblem 1

z + 1.25 = 2.772634127 Simplifying z + 1.25 = 2.772634127 Reorder the terms: 1.25 + z = 2.772634127 Solving 1.25 + z = 2.772634127 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + z = 2.772634127 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + z = 2.772634127 + -1.25 z = 2.772634127 + -1.25 Combine like terms: 2.772634127 + -1.25 = 1.522634127 z = 1.522634127 Simplifying z = 1.522634127

Subproblem 2

z + 1.25 = -2.772634127 Simplifying z + 1.25 = -2.772634127 Reorder the terms: 1.25 + z = -2.772634127 Solving 1.25 + z = -2.772634127 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + z = -2.772634127 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + z = -2.772634127 + -1.25 z = -2.772634127 + -1.25 Combine like terms: -2.772634127 + -1.25 = -4.022634127 z = -4.022634127 Simplifying z = -4.022634127

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.522634127, -4.022634127}

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